Shouldn't the formula be opposite for average calculation? Further, looks like an INNER join should do it for you.
SELECT
(SUM(Inventory.price) / COUNT(Orders.orderid)) AS Orders_Average,
(SUM(Inventory.price) / COUNT(OrderItems.orderid)) AS OrderItems_Average
FROM
ORDERITEMS
INNER JOIN
Inventory ON OrderItems.partid = Inventory.partid
INNER JOIN
Orders ON OrderItems.orderid = Orders.orderid